The paper gives some investigations into a second spectrum of the natural frequency of the flexural vibrations of ships' hulls. Some aspects of the nature of the existence of the second spectrum, the estimate of the frequency of the second spectrum and also the effects of shear flexibility and rotatory linertia force upon the second spectrum of the natural frequency of the vibration of uniform section beam with free ends are investigated as preliminary consideration of hull vibrations of ships in part I. As a numerical example, the spectra of the frequencies of the vertical vibration of the stern of a large tanker considered as a half length of a uniform section beam are illustrated.